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The statistical inference of the alternation of wet and dry periods in daily rainfall records can be achieved through the modelling of inter-arrival time-series, IT, defined as the succession of times elapsed from a rainy day and the one immediately preceding it. In this paper, under the hypothesis that ITs are independent and identically distributed random variables, a modelling framework based on a generalisation of the commonly adopted Bernoulli process is introduced. Within this framework, the capability of three discrete distributions, belonging to the Hurwitz–Lerch-Zeta family, to reproduce the main statistical features of IT time-series was tested. These distributions namely Lerch-series (Lerch), polylogarithmic- series (Polylog) and logarithmic-series (Log) were selected thanks to their capability to describe some peculiar properties usually observed in IT series derived from daily rainfall records: very high standard deviation and skewness, relatively high frequency associated to the unitary IT, monotonically decreasing frequencies with a slow decay. Both Polylog and Log distributions are special cases of the 3-parameter Lerch distribution with a decreasing number of free parameters (2- and 1-parameter, respectively). The analysis, performed on 55 raingauges located in Sicily (Italy) under a typical Mediterranean climate, suggests that a reliable statistical representation of IT can be attained with the 3-parameter Lerch distribution. Despite the marked seasonality of rainfall in the study area, a simple subdivision of the year into two 6-month periods, roughly corresponding to the dry ‘‘semester’’ (D-sem) and the wet ‘‘semester’’ (W-sem), allows a satisfactory reproduction of IT, as well as of wet spells (WS) and dry spells (DS), separately. It was also noticed that the 2-parameter Polylog distribution could be successfully used to reconstruct the DS frequency distribution only. This result suggests that the additional parameter of the Lerch distribution is required by the inclusion of WS into the analysis. Finally, considering that Polylog outperforms the commonly adopted Log, a noteworthy step forward in DS modelling can be achieved by using Polylog distribution rather than Log one.

Correct estimation of crop actual transpiration plays a key-role in precision irrigation scheduling, since crop growth and yield are associated to the water passing through the crop. Objective of the work was to assess how the combined use of micro-meteorological techniques (eddy covariance, EC) and physiological measurements (sap flow, SF) allows a better comprehension of the processes involving in the Soil–Plant–Atmosphere continuum. To this aim, an experimental dataset of actual evapotranspiration, plant transpiration, and soil water content measurements was collected in an olive orchard during the midseason phenological period of 2009 and 2010. It was demonstrated that the joint use of EC and SF techniques is effective to evaluate the components of actual evapotranspiration in an olive orchard characterized by sparse vegetation and a significant fraction of exposed bare soil. The availability of simultaneous soil water content measurements allowed to estimate the crop coefficients and to assess a simple crop water stress index, depending on actual transpiration that can be evaluated even in the absence of direct measurements of actual transpiration. The crop coefficients experimentally determined resulted very similar to those previously evaluated; in particular, in the absence of water stress, a seasonal average value of about 0.65 was obtained for the “single” crop coefficient, whereas values of a 0.34 and 0.41 were observed under limited water availability in the root zone. The comparison between the values of crop water stress index evaluated during the investigated periods evidenced systematically lower values (less crop water stress) in the first year compared to the second, according to the general trend of soil waters content in the root zone. Further researches are however necessary to extent the experimental dataset to periods characterized by values of soil evaporation higher than those observed, in order to verify the crop coefficients even under different conditions than those investigated.

Summary An operational use of the actual evapotranspiration assessed by remote sensing approaches requires the integration of instantaneous fluxes to daily values. This is commonly achieved under the hypotheses of daytime self-preservation of evaporative fraction and negligible daily ground heat flux. The aim of this study is to evaluate the effect of these assumptions on estimate daily evapotranspiration over a full phenological cycle, including phases characterized by significant changes both in net radiation and vegetation cover. To assess the reliability of these hypotheses, the observations made by a flux tower, installed within a homogeneous field of cereal located in the valley part of the Imera Meridionale basin, were analyzed. Additionally, the widely-known SEBAL (Surface Energy Balance Algorithm for Land) model was applied on the same study area by means of four MODIS (MODerate-resolution Imaging Spectroradiometer) images selected across a three-rainfall events period in March–April 2007 with the aim to analyze the consistency of its estimates in an operational study case under different conditions of water availability. The analysis of in situ data highlights errors on 24-h evapotranspiration characterized by an average value of 20% due to daily soil heat flux neglecting; whereas, the hypothesis of evaporative fraction self-preservation causes an average error equal to −16%. Moreover, the analysis of the observations suggests that a compensation effect of the errors related to each hypothesis occurs in most cases (56%), and this makes suitable the approach for practical daily integration purposes. The application of the SEBAL model at basin scale shows a good capability to detect the increase of the actual 24-h evapotranspiration under the tested hypotheses, also in the case of instantaneous evaporative fraction and daily net radiation not derived form in situ observations.

Summary A coupled energy/hydrologic model was applied to simulate the exchange of energy and water in the soil–plant-atmosphere system (SPA). The model, which uses a “two-source” approach to estimate the energy fluxes, and the “force-restore” approach to represent the water balance, was validated by means of evapotranspiration measurements collected via scintillometry and soil moisture measurements collected via time domain reflectometry (TDR) in a Sicilian olive grove. The comparison between measured and estimated fluxes values at an hourly scale showed good agreement. Additional comparisons on a daily timescale confirmed the model’s applicability for quantifying crop water requirements. Also in terms of daily evapotranspiration and soil water content values, the obtained results confirmed the model’s applicability for those practical applications aiming to quantify the crop water requirement. Moreover, further studies should be conducted to test the feasibility of using this model for long term simulations over a broad range of conditions.